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Variétés rationnelles

Horaires : Le vendredi 20 mai 2016, 14h - 15h

Lieu : ENS, salle W

Irreducibility of Polynomials over Number Fields is Diophantine

Philip Dittmann (Oxford)

We show that irreducibility of a polynomial in any number of variables over a number field is a diophantine condition, i.e. captured by an existential formula. This generalises a previous result by Colliot-Thélène and Van Geel that the set of non-nth-powers is diophantine for any n. Our method is heavily based on the Brauer group, originating from Poonen's use of quaternion algebras as a technical tool for first-order definitions in number fields.

 

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